1. Scientific Notation and Significant Figures

2. Going from scientific notation to standard number form. ◦A positive exponent means move the decimal to the right  Ex. 1.34 x 10 4 = 13,400 ◦A negative exponent means move the decimal to the left  Ex. 5.12 x 10 -2 = 0.0512 Now try some!!

3. Going from standard number form to scientific notation Numbers in scientific notation should begin with a number between 1 and 10 and then should be followed by “x 10” with an exponent. ◦Large numbers will have a positive exponent  Ex. 67,000 = 6.7 x 10 4 ◦Small numbers will have a negative exponent  Ex. 0.000031 = 3.1 x 10 -5 Now try some!!!

4. Math with scientific notation! Adding/Subtracting Rules ◦Numbers must have the SAME exponent ◦Then, just add the numbers as normal and keep the original exponent  Ex. 3.3 x 10 3 + 2.1 x 10 3 = 5.4 x 10 3 Now try some!!!

5. Exceptions What if they are not the same?? o If exponents are not the same, one must be adjusted o Example: 7.1 x 10 4 – 2.0 x 10 3 o 7.1 x 10 4 can become 71 x 10 3 o 2.0 x 10 3 can become.2 x 10 4 Now try some!!!

6. Multiplying and Dividing Multiplying ◦When multiplying numbers in scientific notation, the exponents are added  Ex. 3.0 x 10 3 * 2.0 x 10 4 = 6.0 x 10 7 Dividing ◦When dividing numbers in scientific notation, the exponents are subtracted  Ex. 9.0 x 10 5 / 3.0 x 10 2 = 3.0 x 10 3  Ex. 3.0 x 10 3 / 2.0 x 10 4 = 1.5 x 10 -1

7. Significant Figures When rounding, we make certain numbers “insignificant” therefore there are rules with respect to which numbers matter in chemistry These are called “sig figs”

8. The Rules All non-zeros ARE significant ◦Examples: 1.23 has three sig figs 41.12 has four sig figs Zeros between non-zeros ARE significant ◦Examples: 1205 has four sig figs 1.3021 has five sig figs

9. The Rules Placeholder zeros are NOT significant ◦Examples: 34,000 has two sig figs 0.0002 has one sig fig but…. 34,001 has five sig figs… why? Final zeros after a decimal ARE significant ◦Examples: 1.200 has four sig figs 34,000.00 has seven sig figs

10. Practice!! How many sig figs do the following have? ◦3.002 ◦12,000 ◦12,000.00 ◦0.009 ◦12 Now try some!!!

11. Math with Sig Figs Adding/Subtracting ◦Answer should have the same number of DECIMAL PLACES as the original number with the LEAST amount of decimal places  Example: 1.12 + 2.3 = 3.42

12. Math with Sig figs Multiplying/Dividing ◦Answer should have the same number of SIG FIGS as the original number with the LEAST amount of sig figs.  Examples: ◦ 3.40 x 1.2 = 4.08  4.1 ◦ 7 x 24 = 168  200 ◦ 14.000 x 2.00 = 28 = 28.0 ◦ 45,000 x 112 = 5,040,000  5.0 x 10 6